In longitudinal medical studies, multicomponent images of the tissues, acquired at a given stage of a disease, are used to provide information on the fate of the tissues. We propose a quantification of the predictive value of multicomponent images using information theory. To this end, we revisit the predictive information introduced for monodimensional time series and extend it to multicomponent images. The interest of this theoretical approach is illustrated on multicomponent magnetic resonance images acquired on stroke patients at acute and late stages, for which we propose an original and realistic model of noise together with a spatial encoding for the images. We address therefrom very practical questions such as the impact of noise on the predictability, the optimal choice of an observation scale and the predictability gain brought by the addition of imaging components.